Recall that imaginary zeros come in conjugate pairs, so if, for example, 2i is a zero, then - 2i would also be a zero. When we use the zeros of a polynomial to write the polynomial in factored form, we should be writing "a" out front as a leading coefficient. If you expand your polynomial into standard form correctly, the imaginary terms should cancel out. The zeros alone are not enough to narrow our factored polynomial to just one possibility- there are infinite possible "a" values that would create infinite polynomials that contain the known zeros. If we want to find one specific polynomial, we need to know an additional x,y pair that we substitute in to find "a."

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